課程名稱︰普通物理學甲下
課程性質︰系必修
課程教師︰張寶棣
開課學院：電資學院
開課系所︰資訊系
考試日期（年月日）︰2008/06/20
考試時限（分鐘）：140
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Astronomers observe the chromosphere of the Sun with a filter that passes
the red hydrogen spectral line of wave length 656.3nm, called the Hα line.
The filter consists of a transparent dielectric of thickness d held between
two partially aluminized glass plates. The filter is held a constant
temperature. (a) Find the minimum value of d that produces maximum
transmission of perpendicular Hα light, if the dielectric has an index of
refraction of 1.378. (b) What if? If the temperature of the filter increases
above the normal value, what happened to the transmitted wavelength? (Its
index of reflection does not change significantly.) (c) The dielectric will
also pass what near visiable wavelength? One of the glass plate is colored
red to absorb this light? (15%)
2. Monochromatic light is incident on a sheet that has four long narrow
parallel equally spaced slits a distance d apart. (a) Show that the
positions of the interference minima on a screen a large distance L away
from the sheet that has the four equally spaced slits (spacing d, with
d << λ) are given approximately by ym = mλL/4d, where
m = 1,2,3,5,6,7,9,10..., that is, m is not a multiple of 4. (b) For a screen
distance of 2.00m, alight wavelength of 600nm, and a source spaacing of
0.1mm, calculate the width of the principle interference maxima (the
distance between the successive minimum) for four sources. Compare the width
with that for two sources with the same spacing. (10%)
3. (a) How many bright fringes appear between the first diffraction-envelope
minimum the either side of the central maximum in a double slit pattern if
λ = 550nm, d = 0.150mm, and a = 30.0μm? (b) What is the ratioof the
intensity of the third bright fringe to the intensity of the central fringe?
(10%)
4. Narrow, parallel, glowing gas-filled tubes in a variety of colors from block
letters to spell out the name of a night club. Adjacent tubes are all 2.80cm
apart. The tubes froming one letter are filled with neon and radiate
predominantly red light with a wavelength of 640nm. For another letter, the
tubes emit predominantly violet light at 440nm. The pupil of a dark-adapted
viewer's eye is 5.20mm in diameter. If she is in a certain range distance
away, the reviewer can resolve the separate tubes of one color but not the
other. Which color is easier to resolve? Please explain. The viewers's
distance must in what range for her to resolve the tubes of only one color?
(10%)
5. If you double the width of a single slot, the intensity of the light passing
through the slit is doubled. Please show that the intensity at the center of
the screen increases by a factor of 4. Explain why this does not violate the
conservation of energy. (8%)
6. A couple of astronauts left Earth on July 1st, 2010 by taking a spaceship
with speed of 0.95c. The female astronaut realized that she was pregnant
after she took off. After 10 months in her time, she gave birth to a baby
boy. The male astronaut then immediately sent out a request with a speed of
light to people on Earth to request a birth certificate. When did people on
Earth receive his request? What's the birthday of the baby boy in Earth
time? (10%). (Neglect the spaceship acceleration).
7. A particle moves with speed 0.800c in the +x" direction along the x" axis of
frame S", which moves with the same speed and in the same direction along
the x' axis relative to frame S'. Frame S' moves with the same speed and in
the same direction along the x axis relative to frame S. (a) Find the speed
of the particle relative to frame S'. (b) Find the speed of the particle
relative to frame S. (7%)
8. A red light flashes at position xR = 3.00m and time tR = 1.00 * 10E-9s, and
a blue light flashes at xB = 5.00m and tB = 9.00 * 10E-9s, all measured in
the same point as S at t = t' = 0; frame S' moves uniformly to the right.
Both flashes are observed to occur at the same place in S'. (a) Find the
relative speed between S and S'. (b) Find the location of the two flashes in
frame S'. (c) At what time does the red flash occurs in the S' frame? (15%).
9. Let's use the Lorentz diagram to illustrate the pole vaulter puzzle. Assume
that a pole vaulter holds a pole with rest length 4m. He runs through a barn
which has rest width 4m between the first door and second door.
(a) Draw a Lorentz diagram with A-frame as the pole vaulter and B-frame as
the barn. Draw the world lines of the front and back of the pole. And
then draw the world lines of the front and back doors.
(b) Show that in each frame, one will "see" that the length/width of the
moving object is shorter.
(c) Denote the world line intersection of the front pole and the first door
as E0, which is the point that the front pole enters the first door. Do
likewise for the other two intersections as the front pole leaves the
second door (E1) and the back pole enters the first door (E2). Draw
dashed lines from E1(E2) to its projections at tA and tB axes. Show that
when the front pole leaves the second door the pole vaulter "sees" that
the back pole is still outside the first door but the barn people
"thinks" that the back pole is inside the barn. Explain why this is not
a puzzle. (15%)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.242.66